function [VOI, STATES, ALGEBRAIC, CONSTANTS] = mainFunction()
    % This is the "main function".  In Matlab, things work best if you rename this function to match the filename.
   [VOI, STATES, ALGEBRAIC, CONSTANTS] = solveModel();
end

function [algebraicVariableCount] = getAlgebraicVariableCount() 
    % Used later when setting a global variable with the number of algebraic variables.
    % Note: This is not the "main method".  
    algebraicVariableCount =4;
end
% There are a total of 5 entries in each of the rate and state variable arrays.
% There are a total of 22 entries in the constant variable array.
%

function [VOI, STATES, ALGEBRAIC, CONSTANTS] = solveModel()
    % Create ALGEBRAIC of correct size
    global algebraicVariableCount;  algebraicVariableCount = getAlgebraicVariableCount();
    % Initialise constants and state variables
    [INIT_STATES, CONSTANTS] = initConsts;

    % Set timespan to solve over 
    tspan = [0, 10];

    % Set numerical accuracy options for ODE solver
    options = odeset('RelTol', 1e-06, 'AbsTol', 1e-06, 'MaxStep', 1);

    % Solve model with ODE solver
    [VOI, STATES] = ode15s(@(VOI, STATES)computeRates(VOI, STATES, CONSTANTS), tspan, INIT_STATES, options);

    % Compute algebraic variables
    [RATES, ALGEBRAIC] = computeRates(VOI, STATES, CONSTANTS);
    ALGEBRAIC = computeAlgebraic(ALGEBRAIC, CONSTANTS, STATES, VOI);

    % Plot state variables against variable of integration
    [LEGEND_STATES, LEGEND_ALGEBRAIC, LEGEND_VOI, LEGEND_CONSTANTS] = createLegends();
    figure();
    plot(VOI, STATES);
    xlabel(LEGEND_VOI);
    l = legend(LEGEND_STATES);
    set(l,'Interpreter','none');
end

function [LEGEND_STATES, LEGEND_ALGEBRAIC, LEGEND_VOI, LEGEND_CONSTANTS] = createLegends()
    LEGEND_STATES = ''; LEGEND_ALGEBRAIC = ''; LEGEND_VOI = ''; LEGEND_CONSTANTS = '';
    LEGEND_VOI = strpad('time in component environment (day)');
    LEGEND_STATES(:,1) = strpad('R in component R (nanomolar)');
    LEGEND_CONSTANTS(:,1) = strpad('delta_R in component R (first_order_rate_constant)');
    LEGEND_ALGEBRAIC(:,1) = strpad('f1 in component f1 (flux)');
    LEGEND_STATES(:,2) = strpad('U in component U (nanomolar)');
    LEGEND_CONSTANTS(:,2) = strpad('delta_U in component U (first_order_rate_constant)');
    LEGEND_CONSTANTS(:,3) = strpad('alpha0 in component model_parameters (per_nanomolar_day)');
    LEGEND_CONSTANTS(:,4) = strpad('alpha1 in component model_parameters (per_nanomolar_day)');
    LEGEND_CONSTANTS(:,5) = strpad('d01 in component model_parameters (first_order_rate_constant)');
    LEGEND_CONSTANTS(:,6) = strpad('d12 in component model_parameters (first_order_rate_constant)');
    LEGEND_STATES(:,3) = strpad('B1 in component B1 (nanomolar)');
    LEGEND_STATES(:,4) = strpad('B2 in component B2 (nanomolar)');
    LEGEND_ALGEBRAIC(:,3) = strpad('P in component P (nanomolar)');
    LEGEND_ALGEBRAIC(:,4) = strpad('f2 in component f2 (flux)');
    LEGEND_CONSTANTS(:,7) = strpad('delta_b1 in component B1 (first_order_rate_constant)');
    LEGEND_CONSTANTS(:,8) = strpad('delta_b2 in component B2 (first_order_rate_constant)');
    LEGEND_CONSTANTS(:,9) = strpad('PE in component P (nanomolar)');
    LEGEND_ALGEBRAIC(:,2) = strpad('q in component P (dimensionless)');
    LEGEND_CONSTANTS(:,10) = strpad('G in component P (first_order_rate_constant)');
    LEGEND_CONSTANTS(:,11) = strpad('ti in component P (day)');
    LEGEND_CONSTANTS(:,12) = strpad('T in component P (day)');
    LEGEND_CONSTANTS(:,13) = strpad('P0 in component model_parameters (nanomolar)');
    LEGEND_CONSTANTS(:,14) = strpad('a in component f1 (flux)');
    LEGEND_CONSTANTS(:,15) = strpad('a0 in component f1 (flux)');
    LEGEND_CONSTANTS(:,16) = strpad('b in component f1 (nanomolar)');
    LEGEND_CONSTANTS(:,17) = strpad('b0 in component f1 (nanomolar)');
    LEGEND_STATES(:,5) = strpad('x in component x (flux)');
    LEGEND_CONSTANTS(:,18) = strpad('P1 in component x (nanomolar)');
    LEGEND_CONSTANTS(:,19) = strpad('s in component x (nanomolar_day2)');
    LEGEND_CONSTANTS(:,20) = strpad('delta_x in component x (first_order_rate_constant)');
    LEGEND_CONSTANTS(:,21) = strpad('kappa in component f2 (flux)');
    LEGEND_CONSTANTS(:,22) = strpad('kappa0 in component f2 (nanomolar)');
    LEGEND_RATES(:,1) = strpad('d/dt R in component R (nanomolar)');
    LEGEND_RATES(:,2) = strpad('d/dt U in component U (nanomolar)');
    LEGEND_RATES(:,3) = strpad('d/dt B1 in component B1 (nanomolar)');
    LEGEND_RATES(:,4) = strpad('d/dt B2 in component B2 (nanomolar)');
    LEGEND_RATES(:,5) = strpad('d/dt x in component x (flux)');
    LEGEND_STATES  = LEGEND_STATES';
    LEGEND_ALGEBRAIC = LEGEND_ALGEBRAIC';
    LEGEND_RATES = LEGEND_RATES';
    LEGEND_CONSTANTS = LEGEND_CONSTANTS';
end

function [STATES, CONSTANTS] = initConsts()
    VOI = 0; CONSTANTS = []; STATES = []; ALGEBRAIC = [];
    STATES(:,1) = 1.0;
    CONSTANTS(:,1) = 1.905;
    STATES(:,2) = 1.0;
    CONSTANTS(:,2) = 7.5;
    CONSTANTS(:,3) = 4.15;
    CONSTANTS(:,4) = 3.02;
    CONSTANTS(:,5) = 13.0;
    CONSTANTS(:,6) = 4.72E3;
    STATES(:,3) = 1.0;
    STATES(:,4) = 1.0;
    CONSTANTS(:,7) = 7.5;
    CONSTANTS(:,8) = 50.0;
    CONSTANTS(:,9) = 20.55;
    CONSTANTS(:,10) = 35.6;
    CONSTANTS(:,11) = 1.0;
    CONSTANTS(:,12) = 9.0;
    CONSTANTS(:,13) = 0.25;
    CONSTANTS(:,14) = 3.58E5;
    CONSTANTS(:,15) = 2.33E4;
    CONSTANTS(:,16) = 100.0;
    CONSTANTS(:,17) = 263.0;
    STATES(:,5) = 1.0;
    CONSTANTS(:,18) = 20.0;
    CONSTANTS(:,19) = 3.71E5;
    CONSTANTS(:,20) = 0.207;
    CONSTANTS(:,21) = 2.4E5;
    CONSTANTS(:,22) = 6.55E3;
    if (isempty(STATES)), warning('Initial values for states not set');, end
end

function [RATES, ALGEBRAIC] = computeRates(VOI, STATES, CONSTANTS)
    global algebraicVariableCount;
    statesSize = size(STATES);
    statesColumnCount = statesSize(2);
    if ( statesColumnCount == 1)
        STATES = STATES';
        ALGEBRAIC = zeros(1, algebraicVariableCount);
        utilOnes = 1;
    else
        statesRowCount = statesSize(1);
        ALGEBRAIC = zeros(statesRowCount, algebraicVariableCount);
        RATES = zeros(statesRowCount, statesColumnCount);
        utilOnes = ones(statesRowCount, 1);
    end
    RATES(:,4) =  CONSTANTS(:,4).*STATES(:,3).*STATES(:,2) - ( CONSTANTS(:,6).*STATES(:,4)+ CONSTANTS(:,8).*STATES(:,4));
    ALGEBRAIC(:,1) =  CONSTANTS(:,15).*(1.00000 - STATES(:,4)./(CONSTANTS(:,16)+STATES(:,4)))+( STATES(:,5).*(1.00000 - exp( - STATES(:,5)./CONSTANTS(:,14))).*STATES(:,4))./(CONSTANTS(:,17)+STATES(:,4));
    RATES(:,1) = ALGEBRAIC(:,1) -  CONSTANTS(:,1).*STATES(:,1);
    ALGEBRAIC(:,2) = piecewise({VOI<CONSTANTS(:,11), 0.00000 , VOI<CONSTANTS(:,12)+CONSTANTS(:,11)&VOI>=CONSTANTS(:,11), 1.00000 - exp(  - CONSTANTS(:,10).*(VOI - CONSTANTS(:,11))) },  exp( CONSTANTS(:,10).*CONSTANTS(:,12) - 1.00000).*exp( CONSTANTS(:,10).*(VOI - CONSTANTS(:,11))));
    ALGEBRAIC(:,3) = CONSTANTS(:,13)+ CONSTANTS(:,9).*ALGEBRAIC(:,2);
    RATES(:,3) = ( CONSTANTS(:,3).*ALGEBRAIC(:,3).*STATES(:,2)+ CONSTANTS(:,6).*STATES(:,4)) - ( CONSTANTS(:,5).*STATES(:,3)+ CONSTANTS(:,7).*STATES(:,3)+ CONSTANTS(:,4).*STATES(:,3).*STATES(:,2));
    RATES(:,5) = ( CONSTANTS(:,19).*(ALGEBRAIC(:,3) - CONSTANTS(:,13)))./(ALGEBRAIC(:,3)+CONSTANTS(:,18)) -  CONSTANTS(:,20).*STATES(:,5);
    ALGEBRAIC(:,4) = ( CONSTANTS(:,21).*STATES(:,1))./(CONSTANTS(:,22)+STATES(:,1));
    RATES(:,2) = (ALGEBRAIC(:,4)+ CONSTANTS(:,5).*STATES(:,3)+ CONSTANTS(:,6).*STATES(:,4)) - ( CONSTANTS(:,2).*STATES(:,2)+ CONSTANTS(:,3).*ALGEBRAIC(:,3).*STATES(:,2)+ CONSTANTS(:,4).*STATES(:,3).*STATES(:,2));
   RATES = RATES';
end

% Calculate algebraic variables
function ALGEBRAIC = computeAlgebraic(ALGEBRAIC, CONSTANTS, STATES, VOI)
    statesSize = size(STATES);
    statesColumnCount = statesSize(2);
    if ( statesColumnCount == 1)
        STATES = STATES';
        utilOnes = 1;
    else
        statesRowCount = statesSize(1);
        utilOnes = ones(statesRowCount, 1);
    end
    ALGEBRAIC(:,1) =  CONSTANTS(:,15).*(1.00000 - STATES(:,4)./(CONSTANTS(:,16)+STATES(:,4)))+( STATES(:,5).*(1.00000 - exp( - STATES(:,5)./CONSTANTS(:,14))).*STATES(:,4))./(CONSTANTS(:,17)+STATES(:,4));
    ALGEBRAIC(:,2) = piecewise({VOI<CONSTANTS(:,11), 0.00000 , VOI<CONSTANTS(:,12)+CONSTANTS(:,11)&VOI>=CONSTANTS(:,11), 1.00000 - exp(  - CONSTANTS(:,10).*(VOI - CONSTANTS(:,11))) },  exp( CONSTANTS(:,10).*CONSTANTS(:,12) - 1.00000).*exp( CONSTANTS(:,10).*(VOI - CONSTANTS(:,11))));
    ALGEBRAIC(:,3) = CONSTANTS(:,13)+ CONSTANTS(:,9).*ALGEBRAIC(:,2);
    ALGEBRAIC(:,4) = ( CONSTANTS(:,21).*STATES(:,1))./(CONSTANTS(:,22)+STATES(:,1));
end

% Compute result of a piecewise function
function x = piecewise(cases, default)
    set = [0];
    for i = 1:2:length(cases)
        if (length(cases{i+1}) == 1)
            x(cases{i} & ~set,:) = cases{i+1};
        else
            x(cases{i} & ~set,:) = cases{i+1}(cases{i} & ~set);
        end
        set = set | cases{i};
        if(set), break, end
    end
    if (length(default) == 1)
        x(~set,:) = default;
    else
        x(~set,:) = default(~set);
    end
end

% Pad out or shorten strings to a set length
function strout = strpad(strin)
    req_length = 160;
    insize = size(strin,2);
    if insize > req_length
        strout = strin(1:req_length);
    else
        strout = [strin, blanks(req_length - insize)];
    end
end